I implemented a binary splitting algorithm for calculating the digits of pi by following the algorithm on page 2 here: binsplit.pdf
On page 4, the formula for calculating $\frac{1}{\pi}$ is given:
$$ \frac{1}{\pi} = \frac{12}{C^{3/2}} \sum_{n=0}^\infty \frac{(-1)^n(6n)!(A + nB)}{(3n)!n!^3C^{3n}} $$
I was hoping to understand how to arrive at the binary split version below? $$ a(n) = A + nB $$ $$ p(n) = -(6n - 5)(2n - 1)(6n - 1) $$ $$ q(n) = n^3\frac{C^3}{24} $$